Question: Rewrite as a simplified fraction. ${1.1\overline{13} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1113.1313...\\ 10x &= 11.1313...\end{align*}}$ Subtracting the two equations, we have: ${990x = 1102}$ ${x = \dfrac{1102}{990}} $ ${x = \dfrac{551}{495}} \text{or} {1 \dfrac{56}{495}}$